1977 Review by Haines

[TallDave]

The field lines of the sheath get mapped out through the cusp directly to the wall, remember?

This reminds me of tonybarry's magnetic field redering in Vizimag.

viewtopic.php?p=6716&highlight=vizimag#6716

If the fields lines at cusps are that attenuated moving toward the wall, is it reasonable to ask whether they'll succeed in pushing electrons directly up the gradient between wall and Magrid?

[Art Carlson]

Were Haines and Sadowski dealing with plasma in LTE? That might answer some of your questions above.

Is that just your mantra or do you have an idea how that might answer any questions?

[TallDave]

The answer to both your questions is yes.

I'm still not sure what the answer to my question is.

[Solo]

Art: yes, the field lines hit the walls, but if the electrons are low-energy (like the ones produced by ionization of neutrals at the edge of the plasma) then they will not have sufficient energy to reach the wall.

[Art Carlson]

Were Haines and Sadowski dealing with plasma in LTE?

I'm not sure. They don't go into a lot of detail, and it is not obvious that any of the 7 references they cite will be more enlightening. They give the "self-consistent ... pressure balance" as

• p - E^2/8pi = constant

I believe that p is a generalized pressure tensor and does not require the assumption of a Maxwellian distribution. In some previous posts I have tried to come to grips with these issues, e.g. by calculating the electric potential that a non-neutral cusp fan would produce, but I would prefer to see this done by an expert. If you can shed some light on the physics, please do. Better yet, dig up a good review on electrostatic plugging.

For me, the bottom line of this review is Fig. 37, "Reactor scaling for a spindle cusp, with n*tau = 10^15, T = 12 keV, R = a_w = L = sqrt(pi) a for sheath thicknesses 2*(a_e*a_i)^1/2 and 2 a_i in the ring cusp." The smallest radius that meets all the constraints is 2500 m! If I assume the minor physics miracle of a sheath thickness of 2 a_e and the technologically very challenging value of 30 T for the magnetic field, while ignoring the unmanageably huge radiation flux to the wall, I still land at a radius of 50 m.

The biggest loophole I can see, slim though it is, is that electrostatic plugging is somehow possible after all.

[TallDave]

Well, going back to basics here Nebel has said ions rarely make it out to where they would feel a magnetic influence (out where the cusps are) and the whole point of a Polywell is that it's easier to confine electrons than ions, so it makes sense Bussard would ignore papers dealing with cusp confinement of a neutral plasma in LTE with lots of annoyingly heavy ions everywhere, and it also makes sense confinement would be much better for electrons.

I know you don't like the idea of a strongly non-neutral plasma outside the machine, but according the Rick the issue of arcing is fairly complex. Did you give other reasons as well? I can't recall now. Arcing seemed to be Bussard's major concern on the exterior, anyway, which I assume doesn't make sense if the plasma outside is basically neutral.

It's unfortunate there is so much uncertainty about how the machine actually operates; we often seem to spend more time debating that than more interesting (to me, anyway) questions of how the machine, understood in all its basic behaviors, would or would not scale to net power. I hope we get to see the WB-7 results at some point and that they clarify these issues.

[reterry]

It's unfortunate there is so much uncertainty about how the machine actually operates; we often seem to spend more time debating that than more interesting (to me, anyway) questions of how the machine, understood in all its basic behaviors, would or would not scale to net power. I hope we get to see the WB-7 results at some point and that they clarify these issues.

When and how can we anticipate a public release of Nebel's most recent material? There have been lots of statements about it, but has anyone yet actually seen it?

Cheers,
Bob Terry

[MSimon]

Arcing seemed to be Bussard's major concern on the exterior, anyway, which I assume doesn't make sense if the plasma outside is basically neutral.

Metals are neutral. They are conductive. Plasmas are the same. Look up - Paschen Discharge Curve. That will give some hints.

[TallDave]

Oops, right, that occurred to me later; I was thinking in terms of the electron losses. Bussard seems to be talking about electron density on the exterior in that regard (arcing is #3 on his list of e-losses) and then he says this:

n a recirculating MG machine, this factor is important since
it sets the minimum density that can be maintained outside
the machine, for any given interior edge density, as required
for sufficient fusion production. It is desired to keep this
outside density low, in order to avoid exterior Paschen curve
arcing, which can prevent machine operation. To have low
exterior density of electrons, and high interior density
requires large Gwb factors, thus, good Wiffle Ball
confinement is essential to system operation at net power.

I know at some point Rick chimed in that arcing was a fairly complex picture, and a simple Paschen curve did not describe the phenomenon. Still, I'd be curious as to whether we know for sure that the exterior referred to is a cloud of mostly electrons (recirculating/oscillating)as opposed to a neutral plasma.

I would think in the latter case the ions would fly off and be lost, as Bussard described happening when he tried to use repellers in WB-5.

[Art Carlson]

I have pointed out before that Bussard doesn't seem to distinguish between electron density (related to cusp confinement and recirculation) and neutral density (related to arcing). This is one of the reasons that I hold him in low reagrd as a physicist.

[Munchausen]

Well, mister Carlson,

If I can, I will uncover the soft underbelly of the polywell concept and eviscerate it.

there is yet some evisceration to be done here. Frankly, rather than the dreadful predator, I get the picture of a mammoth deeply stuck into a primeval bog of sloppy experimental record and loosely founded theoretical hypothesises.........

The windswept tundra trembles as it occasionally roars and lashes out to stomp a few pescy neanderthals. But from time to time the neanderthals manages to make a spear hit and perhaps they are preparing a big rock up that nearby slope......

Lets for a while assume that the Inverted Bussardian TV with a Constipation is constipated enough: Would that in any way affect your standpoint?

[Art Carlson]

I suspect that Munchausen just made fun of me in a witty and sophisticated way, but I'm to dense to get it. If by some miracle the polywell turns out to be good for something, it would not change the fact that Bussard makes bone chilling errors when he talks about electron and neutral density. It would rather make me think that Sadowski had a good idea several years earlier with his spherical multipole configuration. It looks to me like Bussard either stole that idea or didn't bother to do a decent search of the literature.

[TallDave]

Let's try to be civil, please.

I have pointed out before that Bussard doesn't seem to distinguish between electron density (related to cusp confinement and recirculation) and neutral density (related to arcing).

Well, Bussard mentions both, and refers to "neutrals able to be ionized." I'm guessing that (like Nebel) he found a simple Paschen equation did not describe the phenomenon and just doesn't explain it particularly well in Valencia, which was after all not submitted as a peer-reviewed paper but is merely a talk given at a conference.

Anyways, it seems to me both should matter. Here's my unsophisticated view of the problem: we have a cloud of electrons which has a negative charge. The electrons want to get to the positively-charged Magrid, but the magnetic shielding prevents this. They would also like to get to the wall, which is not shielded by a magnetic field, but has a smaller relative potential difference and is farther away. Now, my understanding of this is admittedly fairly limited, but it seems that in addition to neutral density the size of that charge difference (varying with the density of the electrons) is also going to enter into the equation of whether the electrons overcome resistance and flow into the wall (I don't know if this can be called "arcing" because we're talking about a virtual cathode, but I assume if they have a large enough differential and an easy enough path to the wall they will follow it rather than oscillating/recirculating around the Magrid). Thus we would need to keep electron density below some critical level to prevent this.

If I am making some major errors here, someone please correct me.

[TallDave]

When and how can we anticipate a public release of Nebel's most recent material?

I'm not sure we can. Rick might know, but I'm guessing that decision is in the hands of the funders. They may want to keep it under their hat.

[reterry]

Anyways, it seems to me both should matter. Here's my unsophisticated view of the problem: we have a cloud of electrons which has a negative charge. The electrons want to get to the positively-charged Magrid, but the magnetic shielding prevents this. They would also like to get to the wall, which is not shielded by a magnetic field, but has a smaller relative potential difference and is farther away.

In an ideal confinement field, I suppose, but have not seen demonstrated, that the magnetically insulated electron flow would circulate unimpeded and virtually loss free. For this to happen the outer wall, whatever its potential must be "far" away from the "magrid" and no neutrals can be present to scatter the electron flow. Once any electron orbit intercepts the wall, or the mean free path of a circulating electron falls below its path length to the wall, then the loss processes can produce some avalanche and a subsequent arc.

I would guess that a Pachen description of all this breakdown physics might be inadequate insofar as the electron distribution function may not be Maxwellian due to both inelastic scattering with the neutrals and the global electrostatic confinement potential.

In any case I keenly await a definitive experimental discussion to help sort this stuff out!

Cheers,
Bob Terry